NL

Density and Kinetic Molecular Theory

Mass

  • All matter possesses mass; mass quantifies “how much matter” an object contains.

  • SI‐unit: kilogram (kg)

    • Common laboratory sub-unit: gram (g).

  • Instruments for measuring mass:

    • Triple-beam balance

    • Mass meter

    • Electronic (digital) scale

Volume

  • Volume is the amount of 3-D space occupied.

  • Common laboratory glassware for measuring liquid volume:

    • Measuring cylinder

    • Graduated beaker

    • Measuring (volumetric) flask

    • Burette

    • Pipette

  • Units for regular solids:

    • cubic metre \text{m}^3

    • cubic centimetre \text{cm}^3

    • cubic millimetre \text{mm}^3

  • Units for liquids: millilitre (mL), litre (L).

  • Geometric formula for rectangular solids:

    V = l \times b \times h (length × breadth × height)

  • Equivalences & conversions:

    • 1\,\text{mL} = 1\,\text{cm}^3 ( = 1\,\text{cm} \times 1\,\text{cm} \times 1\,\text{cm} )

    • 1\,\text{L} = 1000\,\text{cm}^3 ( = 10\,\text{cm} \times 10\,\text{cm} \times 10\,\text{cm} )

  • Irregular solid volume: determined by water-displacement (rise in meniscus equals object’s volume).

Density: Concept & Definition

  • Density indicates “mass per unit volume.”

    \text{density} = \frac{\text{mass}}{\text{volume}}

    Common unit sets: \text{g\,mL}^{-1},\; \text{g\,cm}^{-3},\; \text{kg\,L}^{-1}

  • A substance with the largest mass in a fixed volume has the greatest density.

Factors that Determine Density

  • Nature of particles & strength of inter-particle forces.
  • Size/type of the particles.
  • Size of spaces between particles.

Symbol Conventions

  • Mass m ; Volume V ; Density d

    (consistent symbol set used in worked problems)

Unit Consistency Rule

  • If mass is in grams, volume must be mL or cm³.
  • If mass is in kg, volume must be L.

Worked Density Calculations

Example 1

Object: 10\,\text{g} occupies 2.5\,\text{cm}^3

d = \frac{10}{2.5} = 4\,\text{g\,cm}^{-3}

Example 2

Methanol, d = 0.789\,\text{g\,mL}^{-1} fills 200\,\text{mL}.

m=d\times V = 0.789\times200 = 157.8\,\text{g}

Example 3

Copper block: m = 1896\,\text{g} ; l=8.4\,\text{cm},\; b=5.5\,\text{cm},\; h=4.6\,\text{cm}

V = 8.4\times5.5\times4.6 = 212.52\,\text{cm}^3

d = \frac{1896}{212.52} = 8.92\,\text{g\,cm}^{-3}

Irregular Objects & Water-Displacement

  • Principle: Volume of water displaced = volume of object.
Example 4

Initial water: 50\,\text{mL} ; final: 62\,\text{mL}

V_{rock}=62-50=12\,\text{mL}=12\,\text{cm}^3

Example 5

Rock: m = 78\,\text{g},\; V = 47\,\text{mL}

d=\frac{78}{47}=1.66\,\text{g\,mL}^{-1}

Kinetic Molecular Theory (KMT) of Matter

  • Matter comprises tiny particles (atoms/molecules).
  • Six core postulates:
  1. Matter is particulate.
  2. Particles are in perpetual motion.
  3. Empty spaces exist between particles.
  4. Forces of attraction/repulsion act between particles.
  5. Collisions are elastic (no net loss of kinetic energy).
  6. Average kinetic energy \propto temperature and remains constant if T is constant.

Phases & Particle Pictures

Solids
  • Regular lattice, particles touch, vibrate about fixed positions.
  • Properties: incompressible, strong inter-particle forces, rigid shape.
Liquids
  • Random arrangement, small spaces, particles slide past each other.
  • Properties: flow, take container shape, nearly incompressible, moderate forces.
Gases
  • Particles far apart, move rapidly and randomly.
  • Properties: compressible, fill container, negligible forces (ideal gases).

Phase Changes & Terminology

  • Melting (solid→liquid)

  • Freezing (liquid→solid)

  • Evaporation/Boiling (liquid→gas)

  • Condensation (gas→liquid)

  • Sublimation (solid→gas)

  • Deposition (gas→solid)

  • Characteristic temperatures:

    • Melting point

    • Freezing point

    • Boiling point (vapour pressure = atmospheric pressure)

Heating Curve for Water (qualitative)

  1. Ice warming (solid only): T rises.
  2. Melting plateau at 0\,^{\circ}\text{C}: phase change, energy breaks forces.
  3. Liquid warming: T rises.
  4. Boiling plateau at 100\,^{\circ}\text{C}: liquid→gas, energy expands spacing.
  5. Steam warming: gaseous phase, kinetic energy increases.

Room-Temperature Phase Rule

  • If \text{mp} > 25\,^{\circ}\text{C} → substance is solid at room T.
  • If $$\text{bp} ### Diffusion
  • Definition: movement of particles from high concentration → low concentration until uniform.
  • Occurs mainly in liquids & gases; fastest in gases; not in solids (particles fixed).

Gas Pressure (KMT Perspective)

  • Pressure = force of molecular collisions with container walls.
  • Increasing pressure methods:
    • Add more gas (↑ number of collisions).
    • Raise temperature (↑ particle velocity, ↑ collision frequency & force).